From Resonance to Vowels

1. From Resonance to Vowels March 13, 2012

2. Fun Stuff (= tracheotomy) Peter Ladefoged: “To record the pressure of the air associated with stressed as opposed to unstressed syllables we need to record the pressure below the vocal folds. A true recording of the subglottal pressure can be made only by making a tracheal puncture.This is a procedure that must be performed by a physician. A local anesthetic is applied both externally and inside the trachea by means of a fine needle. A larger needle with an internal diameter of 2 mm can then be inserted between the rings of the trachea as shown in figure 3.3”

3. Figure 3.3 “As you can see from my face it is not at all painful. But it is not a procedure that can be carried out in fieldwork situations.”

4. Somewhat Less Fun • Korean stops homework to hand back… • Mystery spectrogram reading exercise #2!

5. Stopping by woods on a snowy evening Whose woods these are I think I know. His house is in the village though. He will not see me stopping here To watch his woods fill up with snow. My little horse must think it queer To stop without a farm house near Between the woods and frozen lake The darkest evening of the year. Robert Frost (1874-1963)

6. Stopping by woods on a snowy evening He gives his harness bells a shake To ask if there is some mistake. The only other sound’s the sweep Of easy wind and downy flake. The woods are lovely, dark and deep. But I have promises to keep, And miles to go before I sleep-- And miles to go before I sleep. Robert Frost (1874-1963)

7. Vowel Resonances • The series of harmonics flows into the vocal tract. • Those harmonics at the “right” frequencies will resonate in the vocal tract. • fn = (2n - 1) * c • 4L • The vocal tract filters the source sound glottis lips

8. “Filters” • In speech, the filter = the vocal tract • This graph represents how much the vocal tract would resonate for sinewaves at every possible frequency: • The resonant frequencies are called formants

9. Source + Filter = Output + This is the source/filter theory of speech production. =

10. Source + Filter(s) F1 F2 F4 F3 Note: F0  160 Hz

11. Schwa at different pitches 100 Hz 120 Hz 150 Hz

12. More Than Schwa • Formant frequencies differ between vowels… • because vowels are produced with different articulatory configurations

13. Remember… • Vowels are articulated with characteristic tongue and lip shapes.

14. Vowel Dimensions • For this reason, vowels have traditionally been described according to four (pseudo-)articulatory parameters: • Height (of tongue) • Front/Back (of tongue) • Rounding (of lips) • Tense/Lax = amount of effort? = muscle tension?

15. The Vowel Space The Vowel Space o

16. Formants and the Vowel Space • It turns out that we can get to the same diagram in a different way… • Acoustically, vowels are primarily distinguished by their first two formant frequencies: F1 and F2 • F1 corresponds to vowel height: • lower F1 = higher vowel • higher F1 = lower vowel • F2 corresponds to front/backness: • higher F2 = fronter vowel • lower F2 = backer vowel

17. [i] [u] [æ] (From some old phonetics class data)

18. [i] [u] [æ] (From some old phonetics class data)

19. (From some old phonetics class data)

20. Women and Men • Both source and filter characteristics differ reliably between men and women • F0: depends on length of vocal folds • shorter in women  higher average F0 • longer in men  lower average F0 • Formants: depend on length of vocal tract • shorter in women  higher formant frequencies • longer in men  lower formant frequencies

21. Prototypical Voices • Andre the Giant: (very) low F0, low formant frequencies • Goldie Hawn: high F0, high formant frequencies

22. F0/Formant mismatches • The fact that source and filter characteristics are independent of each other… • means that there can sometimes be source and filter “mismatches” in men and women. • What would high F0 combined with low formant frequencies sound like? • Answer: Julia Child.

23. F0/Formant mismatches • Another high F0, low formants example: • Roy Forbes, of Roy’s Record Room (on CKUA 93.7 FM) • The opposite mis-match = • Popeye: low F0, high formant frequencies

24. Back to Vowels • A vowel space is defined by a speaker’s range of first formant (F1) and second formant (F2) frequencies. • …but everybody’s vowel space is different. • Vowels contrast with each other in terms of their relationships within that acoustic space. • F1 determines the “height” of vowels. • F2 determines the “front/backness” of vowels. • Question: • How does the way that vowels are produced… • Determine their acoustic characteristics?

25. Articulation to Acoustics • Last time, we calculated the formant values for “schwa”, or a neutral vowel. • Theoretical values (vocal tract length = 17.5 cm) • F1 = 500 Hz • F2 = 1500 Hz • F3 = 2500 Hz • My values: • F1 = 500 Hz • F2 = 1533 Hz • F3 = 2681 Hz • F4 = 3498 Hz

26. With a neutral vowel, we’re somewhere in the middle of the acoustic vowel space. Q: How do we get to the corners of the space?

27. Perturbation Theory • There are two important theories that answer this question. • The first of these is Perturbation Theory. • Remember: formants are resonances of the vocal tract. • These resonances are the product of standing waves in the resonating tube of the articulatory tract. glottis lips

28. What’s the Big Idea? • Chiba and Kajiyama (1941): • Formant frequencies can be changed by perturbing the airflow of the standing waves in the vocal tract • Idea #1: velocity of standing waves is inversely related to pressure • Sort of like the Bernoulli Effect

29. Standing Waves in the Vocal Tract • Remember: • Vocal tract is a tube with one open end at the lips. • So: • Pressure node at the lips • Pressure anti-node at the glottis • …for all potential standing waves • This translates into: • Velocity anti-node at the lips • Velocity node at the glottis

30. Standing Waves in the Vocal Tract • Diagrammed in terms of velocity: F1 F2

31. The Big Idea, part 2 • Idea #2: constriction at (or near) a velocity anti-nodedecreases frequency • The constriction slows the velocity down •  constriction at a pressure node decreases frequency • Idea #3: constriction at (or near) a velocity nodeincreases frequency • The constriction increases the pressure • This enhances airflow •  constriction at a pressure anti-node increases frequency

32. Here’s the goal • Let’s figure out how we can perturb the airflow in the articulatory tract to get to the corners of the vowel space. • We need to: • Lower F1 and raise F2 --> high, front vowels • Lower F1 and lower F2 --> high, back vowels • Raise F1 and raise F2 --> low, front vowels • Raise F1 and lower F2 --> low, back vowels • Let’s consider them each in turn…

33. F1 • Velocity node at glottis • Velocity anti-node at lips • To lower F1: • make a constriction closer to the lips than to the glottis • To raise F1: • make a constriction closer to the glottis than to the lips

34. F2 • Velocity nodes at: • palate • glottis • Velocity anti-nodes at: • lips • pharynx

35. F2 • To raise F2, make a constriction at the: • palate • glottis • To lower F2, make a constriction at the: • lips • pharynx

36. 1. High, Front Vowels • Lower F1 and raise F2 • Where should we make a constriction(s)?

37. 1. High, Front Vowels • Lower F1 and raise F2 • Where should we make a constriction(s)? • To lower F1:

38. 1. High, Front Vowels • Lower F1 and raise F2 • Where should we make a constriction(s)? • To lower F1: • constrict close to lips

39. 1. High, Front Vowels • Lower F1 and raise F2 • Where should we make a constriction(s)? • To lower F1: • constrict close to lips • To raise F2:

40. 1. High, Front Vowels • Lower F1 and raise F2 • Where should we make a constriction(s)? • To lower F1: • constrict close to lips • To raise F2: • constrict at palate

41. 2. High, Back Vowels • = Lower F1 and lower F2 • Where should we make a constriction(s)?

42. 2. High, Back Vowels • = Lower F1 and lower F2 • Where should we make a constriction(s)? • To lower F1:

43. 2. High, Back Vowels • = Lower F1 and lower F2 • Where should we make a constriction(s)? • To lower F1: • constrict at lips

44. 2. High, Back Vowels • = Lower F1 and lower F2 • Where should we make a constriction(s)? • To lower F1: • constrict at lips • To lower F2:

45. 2. High, Back Vowels • = Lower F1 and lower F2 • Where should we make a constriction(s)? • To lower F1: • constrict at lips • To lower F2: • constrict at lips • constrict at “pharynx” • Note: these vowels are usually rounded